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Existence of a weak solution to a nonlinear fluid-structure interaction problem with heat exchange

In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which is filled with a fluid governed by the full Navier-Stokes-Fourier system. The fluid and the shell are fully coupled, giving rise to a novel nonlinear moving boundary fluid-structure interaction problem involving heat exchange. The existence of a weak solution is obtained by combining three approximation techniques -- decoupling, penalization and domain extension. This approximation scheme allows us to use the methods already developed for fluids on moving domains, thus drastically simplifying the analysis at hand.